Acceleration of Numerical Integration of the Equations of Motion of Asteroids

Solar System Research - Finding and studying possible collisions of asteroids approaching the Earth requires a significant amount of computation. This paper describes the R0 program created to...     

Observations of the intensity of the penumbra of sunspots

Observations of the penumbral intensity of sunspots in 13 wavelength regions are presented. In 4 wavelength regions 54 sunspots are measured. In the other wavelength regions the number of sunspots considered ranges from 3–19.The penumbral intensity alters with position within the spot. This intensity variation is found to be comparable with the change in intensity from one spot to another. The penumbral intensity is found to be independent of spot size in the sample considered.The penumbra model of Kjeldseth Moe and Maltby (1969) with = 0.055 is supported by the measurements.     

Equation of state and anisotropy of pressure of magnetars

Magnetars are the neutron stars with the highest magnetic fields up to 10¹⁵–10¹⁶ G. It has been proposed that they are also responsible for a variety of extra-galactic phenomena, ranging from giant flares in nearby galaxies to fast radio bursts. Utilizing a relativistic mean field model and a variable magnetic field configuration, we investigate the effects of strong magnetic fields on the equation of state and anisotropy of pressure of magnetars. It is found that the mass and radius of low-mass magnetars are weakly enhanced under the action of the strong magnetic field, and the anisotropy of pressure can be ignored. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars.     

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF₃₁, were discovered, librating about the L₅ Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ₇, to be a Trojan, associated with the L₄ Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND₄₃) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW₁₅ and 2000 TG₂, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.     

Graphical representation of periodic motion of the line of nodes of the Moon

In the text-books of astronomy, sections generally related to the Moon deal with the orbital elements of the Earth-Moon system such asa, e, i, , and the time of perigee passage. While the MEAN of the first of the three elements do not vary, mean longitude of the ascending node-mean longitude of the lunar perigee and the time of perigee passage undergoes secular as well as periodic changes due predominantly to the action of the Sun's gravitational attraction. While to a certain degree, explanations related to the calculation of the lunar orbit parameters are given, not a single graphical representation of these short- or long-periodic changes are presented. We allow the number of data related to these periodic changes must cover a large span of time; and if regression of the line of nodes or advances of the line of apses are to be graphically seen, data covering 18.61 and 8.85 yr, respectively, are needed. In this work we particularly aim at the graphical representation of the periodic changes of the line of nodes.